Reentrant fluid phase

There are some early speculations [106] and more recent indications [112, 156] that a reentrant fluid phase (RF) exists for N2 on graphite, which is squeezed in between the commensurate (CD) and triangular incommensurate (ID) disordered phases just above monolayer completion and temperatures of about 50-80 K (see Fig. 46 in Section in.E). But it is not fully clear how the strip of the reentrant fluid extends down to low temperatures and where this fluid undergoes solidification. 

Figure 46. Phase diagram of N2 on graphite based on adiabatic heat capacity data coverage is reported in units of the complete n/S monolayer. Orientationally ordered commensurate phase (CO), orientationally disordered commensurate phase (CD), orientationally ordered uniaxially compressed incommensurate phase (UIO), orientationally disordered uni-axially compressed incommensurate phase (UID), triangular compressed incommensurate phase (TI), fluid phase (F), speculative reentrant fluid phase (RF). The measurement path for the highest coverage in Fig. 45 is sketched by the dashed line. (Adapted from Fig. 10 of Ref. 156.)...

Figure 47. Phase diagram of N2 on boron nitride based on adsorption isotherms coverage is repotted in units of the complete Vs mono-layer obtained from the top of the fluid to commensurate solid isotherm substep at low temperatures less than 51 K. Commensurate solid phase (C), fluid phase (F), reentrant fluid phase (RF). The solid lines correspond to phase boundaries based on measured features, the dotted line is an expected phase boundary, and the triangle marks the tricritical point. Second-layer growth instead of a transition to an incommensurate solid phase is expected beyond the reentrant fluid phase in the temperature range studied. (Adapted from Fig. 4 of Ref. 1.)...

An incommensurate solid to a reentrant fluid transition and a reentrant fluid to commensurate transition, both being of second order. In particular, the existence of a novel reentrant fluid phase separating the commensurate and incommensurate phases constitutes clearly one of the most spectacular and interesting phenomena observed in the study of rare gases adsorbed on graphite. Another important result is that there is no multicritical (commensurate-incommensurate fluid) point at high temperatures. 

With respect to the computer simulations of helium on graphite, we would only note that they reproduce the presence of fluid, commensurate and incommensurate solids, and a reentrant fluid phase [238,325]. The phase diagram obtained is similar to that proposed by Ecke and Dash [237], which differs from the more recent proposal of Greywall [106] (Fig. 7) and does not include a liquid-vapor transition. 

Figure 4.14. Phase diagram, coverage vs. temperature, of N2 physisorbed on graphite. Symbols used fluid without any positional or orientational order (F), reentrant fluid (RF), commensurate orientationally disordered solid (CD), commensurate herringbone ordered solid (HB), uniaxial incommensurate orientation-ally ordered (UlO) and disordered (UID) solid, triangular incommensurate orientationally ordered (lO) and disordered (ID) solid, second-layer liquid (2L), second-layer vapour (2V), second-layer fluid (2F), bilayer orientationally ordered (2SO) and disordered (2SD) solid. Solid lines are based on experimental results whereas the dashed lines are speculative. Adapted from Marx Wiechert, 1996.

Although these simplified models of hydrogen-bonded systems give a far from complete picture of the solid-fluid phase behavior of water, this kind of approach to identifying the key features required in the molecular model is an instructive one. Indeed, the inability of the PMW to generate reentrant melting of the low-density solid at thermodynamically stable states is an important result. It shows us that more than just short-range directional forces are required for this to occur. 

Figure 48. Semilogarithmic plot of the isothermal compressibility of N2 on boron nitride at 60.8 K as a function of the coverage in units of the complete /3 monolayer. The peak sequence starting at low coverages is attributed to the fluid to commensurate solid F-C and commensurate solid to reentrant fluid C-RF transitions and finally to second-layer growth RF-B (instead of a transition from the reentrant fluid to an incommensurate solid phase). (Adapted from Fig. 5 of Ref. 1.)...

Figure 51. Experimental phase diagram of CO physisorbed on graphite with the phases fluid (F), commensurate (CD) and incommensurate (ID) orientationaliy disordered solids, reentrant fluid (RF), second-layer fluid (2F), vapor (2V), liquid (2L), and orientationaliy disordered solid (2SD) phases. Filled circles and triangles represent phase boundary locations from heat capacity and vapor pressure measurements, respectively. Solid and dashed lines indieate phase boundaries believed to be associated with first-order and continuous transitions, respectively dash-dotted lines correspond to speculated boundaries. The large filled triangle and the large filled circle mark the two-dimensional Potts tricritical and critical points, respectively the tricritical point marked with an open triangle is tentative. Lines I-VII with arrows are experimental paths of the heat capacity scans shown in Fig. 52. Coverage unity corresponds to a coverage of CO forming a complete (Vs x VS) monolayer. (Adapted from Fig. 1 of Ref. 112.)...

The freezing transition from the reentrant fluid to the commensurate solid monolayer seems to be of first order at low temperatures and changes to a continuous transition at a tricritical point near 85 K. This interpretation of the heat capacity and compressibility data [112], however, needs further experimental confirmation, and the corresponding tricritical point shown in the phase diagram Fig. 51 as an open triangle is only tentative. There are also conflicting theoretical predictions concerning the order of the RF - CD transition [77, 78, 151, 260], and the present resolution of the calorimetric data [112] does not allow us to draw a firm conclusion in this respect. 

Figure 64. Partly speculative phase diagram of CO on graphite obtained from adiabatic heat capacity measurements [156]. The phases are commensurate (C), uniaxial incommensurate (UI), triangular incommensurate pinwheel (PW), fluid (F), and reentrant fluid (RF). (Adapted from Fig. 11 of Ref. 156.)...

Fig. 4. Reentrant fluid of Kr/graphite. High T region of the Kr/graphite phase diagram (from Ref. 30). The reentrant fluid (RF) phase is a domain wall fluid bounded by commensurate (C) and incommensurate (IC) regimes. S(23D) and L(3D) are the bulk solid and hquid phases. Sohd lines denote first-order transitions and dashed lines denote continuous transitions.

At extremely low temperatures, we observe that the miscibility gap starts to split again at the point E in the center of the concentration axis, and a new homogeneous microphase (shown by MS ) is stabilized in between. Such a low-temperature microphase (called a reentrant microphase) is stabilized simply because the population of block copolymers becomes so large in this low-temperature region that they homogenize the two demixed fluid phases into a single one. 

Ionic miaogels can reveal an ultra-soft interaction potential that leads to peculiar struaure formation already in the fluid phase. Figure 26(a) displays the calculated stmcture factor for different densities and an anomalous behavior of peak height and position with increasing density is observed. The soft interaction potential leads to a rich phase behavior with a transition from fee to bcc structure and reentrant melting transitions, see Figure 26(b). 

For a long time, there were major imcertainties about the commensurate-incommensurate phase transition, mainly because the experimental studies indicated a different order of that transition at high and low temperatures [113]. These uncertainties have been resolved by the proven existence of a reentrant fluid between the two solid regions [15,143]. The final proposed form for the phase diagram is shown in Fig. 5 [144], where the points are experimental data obtained from thermodynamic methods. 

FIG. 6 Pressure-teniperature phase diagram for krypton on graphite near the monolayer completion, proposed hy Specht et al. [143] fiom x-ray diffraction data. Dashed lines indicate the scans that were made in experiments. Triangles are from Ref. 137. (F = fluid, C = commensurate fluid, IC = incommensurate solid, RF = reentrant fluid, L = bulk liquid, S = bulk solid.)... 

A clear disadvantage of the earliest lattice models [181] (and of density functional approaches) is that only commensurate solid phases (in addition to the fluid phases, obviously) are considered. A more complex lattice model including incommensurate phases has been developed by Caflisch et al. [144] for the particular case of Kr on graphite. The experimentally observed phase diagram, including the presence of the reentrant fluid is reproduced, as is shown in Fig. 5, where the lines indicate the Caflisch et al. [144] theoretical results. Although the application of this model to other systems seems possible, it could be very laborious. 

Liquid polymorphism in one-component fluids is an example of so-called anomalous phase behavior. This term is used to emphasized the difference with respect to the normal behavior characterizing prototypical (i.e., argon like) simple liquids. Anomalous behavior includes, in addition to polymorphism in the liquid and solid phases, reentrant melting, that is, melting by compression at constant temperature, and a number of other thermodynamic, dynamic, and structural anomalies, as, for example, the density anomaly (a decrease in density upon cooling), the diffusion anomaly (an increase of diffusivity upon pressurizing), and the structural anomaly (a decrease of structural order for increasing pressure). 

---